Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions

One-shot devices, such as rockets, airbags of automobiles, and electro-explosive devices, can be used only once and will be extensively destroyed. The actual lifetimes of the devices cannot be observed, no matter whether the outcomes are successful or not. Step-stress accelerated life tests, which are useful for shortening the lifetimes of devices and quickly collecting lifetime data in a limited time, are widely adopted in engineering reliability studies. However, optimal designs of step-stress accelerated life tests for one-shot devices have not been well studied. This paper provides a procedure of determining optimal designs of simple step-stress accelerated life tests for one-shot devices by minimizing the asymptotic variance of the maximum likelihood estimate of reliability at normal operating conditions under Weibull distributions, with respect to inspection times and sample allocations. Comprehensive simulation studies are carried out to study the optimal designs under Weibull distributions with various hazard rates, showing that the optimal designs can maintain the simulated standard deviations at the nominal level of standard error. Besides, sensitivity analysis is conducted to evaluate the robustness of determined designs when mis-specification on planning values of model parameters exists. Finally, an application in grease-based magnetorheological fluids is presented to illustrate the optimal designs.